Nonlinear stress wave generation model as an earthquake precursor


A network of vertical static pendulums (tiltmeters) has been in operation in Central Europe since July 2007. Hundred and eighty three seismic events of magnitude 7 and greater have occurred worldwide (EMSC) during the ten-year period. Several kinds of tilt anomalies were recognised within days up to months before the mainshocks. The most typical anomaly was a sudden tilting, parallel with the geologic structure, where the pendulum was installed. Based on the observations, we are proposing an asperity model, explaining the generation of so called “stress waves” before the mainshocks. Such stress waves of very low frequency (i.e. periods of days up to the first months) could be detected anywhere on the globe, especially on active geological structures, parallel with the fault, where a mainshock can happen. The observations suggest that we could estimate that part of the global fault system, which generates the detected stress wave, and which reaches the critical state. The estimation can be performed according to the amplitude of the stress wave, compared with stress waves detected on other structures of different orientations. According to the length of the stress wave (its period) and the tilt amplitude, it could be possible to estimate the magnitude of the mainshock.


  1. 1.

    P. Bak, C. Tang, J. Geophys. Res. 94, 15635 (1989)

    ADS  Article  Google Scholar 

  2. 2.

    N.M. Beeler, D.A. Lockner, J. Geophys. Res. 108, 2391 (2003)

    ADS  Article  Google Scholar 

  3. 3.

    J.N. Brune, J. Geophys. Res. 73, 777 (1968)

    ADS  Article  Google Scholar 

  4. 4.

    S. Crampin, Y. Gao, A global earthquake monitoring system that would stress forecast all damaging earthquakes worldwide, in Proc. of ISESEP, 8th July, 2009, Beijing (2009).

  5. 5.

    A. Douglas, J.A. Hudson, R.G. Pearce, Bull. Seismol. Soc. Am. 78, 1367 (1988)

    Google Scholar 

  6. 6.

    Pendulum network data: dynamicgravity (2018),

  7. 7.

    K. Eftaxias, P. Kapiris, J. Polygiannakis, A. Peratzakis, J. Kopanas, G. Antonopoulos, D. Rigas, Nat. Hazards Earth Syst. Sci. 3, 217 (2003)

    ADS  Article  Google Scholar 

  8. 8.

    R.J. Geller, D.D. Jackson, Y.Y. Kagan, F. Mulargia, Science 275, 1616 (1997)

    Article  Google Scholar 

  9. 9.

    K. Holub, P. Kalenda, J. Rušajová, Terr. Atmos. Ocean. Sci. 24, 933 (2013)

    Article  Google Scholar 

  10. 10.

    V. Jirásek, O dolován černého uhl v oblasti Rtyňsko-Bohdašnské na Jestřebch horách (Rtyně v Podkrkonoš, 2012), p. 186

  11. 11.

    P. Kalenda, I. Pompura, Acta Montana 102, 145 (1997)

    Google Scholar 

  12. 12.

    P. Kalenda, L. Neumann, I. Wandrol, Indirect stress measurement by static vertical pendulum, in Proc. of 47th Int. Sci. Conf. Experimentáln analýza napět (TU, Liberec, 2009), pp. 120–128

  13. 13.

    P. Kalenda, L. Neumann, Static vertical pendulum – observations of anomalous tilt before earthquakes (case study), in Rock stress and earthquakes, edited by F. Xie (2010), pp. 795–803

  14. 14.

    P. Kalenda, L. Neumann, J. Málek, L. Skalský, V. Procházka, L. Ostřihanský, T. Kopf, I. Wandrol, Tilts, global tectonics and earthquake prediction (SWB, London, 2012), p. 247

  15. 15.

    P. Kalenda, D. Ouzounov, V. Bobrovskiy, L. Neumann, O. Boborykina, A. Nazarevych, S. Šebela, J. Kvetko, W.-B. Shen, Geophys. Res. Abstr. 15 (2013)

  16. 16.

    P. Kalenda, K. Holub, J. Rušajová, L. Neumann, NCGT 1, 38 (2013b)

    Google Scholar 

  17. 17.

    P. Kalenda, D. Ouzounov, Geophys. Res. Abstr. 16 (2014)

  18. 18.

    P. Kalenda, D. Ouzounov, V. Bobrovskiy, L. Neumann, O. Boborykina, A. Nazarevych, S. Šebela, J. Kvetko, W.-B. Shen, Multiparameter observations of precursors before strong earthquakes, in Proc. Of International Scientific Spring (March 10–14, 2014), Islamabad, Pakistan (2014)

  19. 19.

    P. Kalenda, I. Wandrol, K. Holub, J. Rušajová, TAO 26, 103 (2015)

    Google Scholar 

  20. 20.

    P. Kalenda, L. Neumann, D. Ouzounov, The precursors before the strongest earthquakes 2007–2015 show: an effective short-term prediction is a real scientific goal, in Proc, in Proc. Of International Conference of Geoethics 2015 Prague – Přbram – Prague October 9 – 19 (2015)

  21. 21.

    P. Kolnský, J. Valenta, R. Gaždová, Acta Geodyn. Geomater. 9, 191 (2012)

    Google Scholar 

  22. 22.

    T. Lay, T.C. Wallace, Modern global seismology (Academic Press, San Diego, 1995), p. 521

  23. 23.

    P. Mandal, B.K. Rastogi, R.K. Chadha, H.V.S. Satyanarayana, S.P.C. Sarma, N. Kumar, Ch Satyamurthy, P.I. Raju, N.A. Rao, Method of short term forecasting of moderate size earthquakes, US Patent No. 6728640 (2004)

  24. 24.

    V.I. Mjachkin, W.F. Brace, G.A. Sobolev, J.H. Dieterich, PAGEOPH 113, 169 (1975)

    Article  Google Scholar 

  25. 25.

    L. Neumann, P. Kalenda, Static vertical pendulum – apparatus for in-situ relative stress measurement, in Rock Stress and Earthquakes, edited by F. Xie (2010), pp. 255–261

  26. 26.

    F. Qian, B. Zhao, W. Qian, J. Zhao, S.-G. He, H.-K. Zhang, S.-Y. Li, S.-K. Li, G.-L. Yan, Ch-M Wang, Z.-K. Sun, D.-N. Zhang, J. Lu, P. Zhang, G.-J. Yang, J.-L. Sun, Ch-S Guo, Y.-X. Tang, J.-M. Xu, K.-T. Xia, H. Ju, B.-H. Yin, M. Li, D.-S. Yang, W.-L. Qi, T.-M. He, H.-P. Guan, Y.-L. Zhao, Sci. Chin. Ser. D: Earth Sci. 52, 1572 (2009)

    ADS  Article  Google Scholar 

  27. 27.

    D. Ouzounov, K. Hattori, P. Kalenda, W.-B. Shen, V. Bobrovkiy, M. Kafatos, Monitoring mega earthquake disasters by integrating multi-parameter and multi-sensors observation from ground and space, in APSCO Third International Symposium on Earth Quake Monitoring and Early Warning by Using Space Technology, 13–15 September 2011 (Friendship Hotel Beijing, China, 2011)

  28. 28.

    D. Ouzounov, S. Pulinets, K. Hattori, L. Lee, J.Y. Liu, P. Kalenda, Multi-sensor observation of pre-earthquake signals and their connection with major seismicity (IUGG, 2015). Abstract IUGG-2669

  29. 29.

    T. Rikitake, Earthquake Prediction (Elsevier Scientific Pub, Amsterdam, Netherlands, 1976)

  30. 30.

    Ch Scholz, L.R. Syke, Y.P. Aggarwal, Science 181, 803 (1973)

    ADS  Article  Google Scholar 

  31. 31.

    A. Sornette, D. Sornette, Europhys. Lett. 9, 197 (1989)

    ADS  Article  Google Scholar 

  32. 32.

    I. Tsubokawa, J. Geod. Soc. Jpn. 19, 116 (1973)

    Google Scholar 

  33. 33.

    I. Wandrol, Modelling of mechanical behavior of the Earth’s crust (Ostrava, 2017), p. 160. Dissertation thesis. VŠB - Technical University of Ostrava, Faculty of Mechanical Engineering. Advisor Karel Frydrýšek

  34. 34.

    S. Wei, Eng. Sci. 9, 7 (2007)

    Google Scholar 

  35. 35.

    M. Wyss, A.C. Johnston, F.W. Klein, Nature 289, 231 (1981)

    ADS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to P. Kalenda.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kalenda, P., Neumann, L. Nonlinear stress wave generation model as an earthquake precursor. Eur. Phys. J. Spec. Top. 230, 353–365 (2021).

Download citation